Suppose a=8 b=8√3

Question

a. If γ = 90◦, solve the triangle.

b. If c = 9(1 +√3), how many triangles can be formed? If there are none, explain why.

Otherwise, solve the triangle/s.

c. If α = 30◦ what are the possible values for β?

Answer 1

a) 90-60-30, 16-8sqr3-8

use law of cosines or pythagorean theorem

c^2= 64+192-128sqr3Cos90= 256, c=sqr256=16

c^2=a^2+b^2=256

c=16

then use law of sines

or

just recognize it's a right triangle, 90-60-30 degrees

with opposite sides in a ratio of 2-sqr3-1 multplied by 8

b) zero triangles

has to be either 0,1 or 2

use the law of cosines to find C

c^2=a^2+b^2-2abCosC

81(1+2sqr3+3)=64+192-2(8)(8sqr3)CosC

81+162sqr3+243=256-128sqr3CosC

CosC= (324-256+162sqr3)/-128sqr3=-68/128sqr3-162/128=-17/32sqr3- 41/32<-1

C DNE

C Does Not Exist

0 triangles

as cosines are never <-1

c) sin30/8-sinB/8sqr3

1/2=sinB/sqr3

sinB=sqr3/2

B=60, 120 degrees